In a measuring cup, combine the lime juice, mustard, honey, garlic, jalapeño, cilantro stems, oil, cumin, and salt. Blend with an immersion blender or upright blender until smooth.
With a sharp knife, butterfly the chicken breast to flatten and make it more even. Pour ½ cup of the dressing over the chicken breast as a marinade. Cover and keep refrigerated for 30 minutes or up to 1 hour.
Heat 1 tbsp neutral oil in a skillet over medium heat, 2 minutes. Add the marinated chicken breast, one at a time. Sear until browned and the temperature registers 160°F. Once the chicken has been cooked, add the prepared onion and peppers to the skillet. Sprinkle with salt and cumin. Sauté until the vegetables are just tender, 4-6 minutes. Add the minced jalapeño and garlic. Continue to cook for 1 minute. Add the drained and rinsed beans. Cook until the beans are just warmed through, 1-2 minutes.
Remove the vegetables and beans from the heat. Slice the chicken into strips and squeeze some fresh lime juice over the meat and sliced avocado. Chop the romaine and place it on a large platter. Drizzle with the remaining dressing to taste, as little or as much as desired. Mix with the lettuce. Add the prepared peppers, onion, and beans. Top with chicken, avocado, and cilantro. Serve with tortilla chips on the side.